Order Degree Evaluation of Information System Based on Improved Structural Entropy

http://dx.doi.org/10.4236/ojbm.2015.33023

Order Degree Evaluation of Information

System Based on Improved Structural

Entropy

Zhiting Song, Peipei Liang, Li Ni

School of Business Administration, South China University of Technology, Guangzhou, China Email: szt05_scut@163.com, 614lpp@163.com, riskll@qq.com

Received 20 April 2015; accepted 2 June 2015; published 5 June 2015

Copyright © 2015 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Abstract

To solve the problem that available methods of order degree evaluation ignore the heterogeneous information interactions between subsystems, an improved method of order degree evaluation, based on structural entropy, is proposed from the perspective of heterogeneous interactions be-tween subsystems. A case study is proposed to test our model, and order degree under the two scenarios is contrasted. Result shows that directed information flow increases timeliness of in-formation and decreases accuracy of inin-formation, which is repeatedly verified in practice. The proposed model, which is more in line with the actual structure of information system, not only further improves order degree evaluation in theory, but also provides operational method to or-der degree evaluation in real-world information systems.

Keywords

Order Degree, Information System, Structural Entropy, Directed Information Flow

1. Introduction

plays a vital role in the stable operation of information systems.

Currently, there exist two major methods to compute order degree of systems: 1) multiple independent order parameters are selected to determine multi-dimensional order degree at the macro level [3]; 2) at the micro level, system entropy is measured to reflect order degree [4]. The paper studies how directed information flow between subsystems affects order degree of systems; entropy is thus applied to evaluate order degree of systems. For ge-neralized information systems, entropy can be used to measure disorder degree of systems. High entropy denotes that information system cannot obtain or utilize information effectively, which results in a huge loss of informa-tion in informainforma-tion systems. Entropy has been widely used to evaluate order degree of various systems or orga-nizational structures. Shannon [5] first proposes quantitative information entropy to measure order degree of systems. Literature [6] [7] homogenizes information and resource flow and then puts forward structural entropy to measure order degree of organizational structure. Structural entropy is also used to evaluate order degree of cellular manufacturing systems and manufacturing resource organization modes [8] [9]. Furthermore, structural entropy can be applied to many other systems such as supply chain system and biological system [10] [11].

Literature above is based on homogeneous interactions between subsystems which are heterogeneous in real-ity. For example, information flow is directed in information systems. Our work builds on this literature and ex-tends structural entropy to incorporate directed information flow required to evaluate order degree of informa-tion systems. Finally, a case study is given to test the method.

2. Analysis of Original Structural Entropy Model

Literature [6] presents structural entropy model to evaluate order degree of system structure shown in Figure 1(a). The structure entropy model is briefly introduced as follows. In Figure 1(a), the set of system elements is

1 2 { , , , n}

V = v v v where vi (1 ≤ i≤ n) is a subsystem. Let L(vi, vj) denotes the length of shortest path between

subsystems vi and vj. If vi and vj are directly connected, L(vi, vj) = 1. Otherwise, let L(vi, vj) increase by one for

each transfer. W(vi) is the number of the subsystems that directly linked with vi. According to the definition of

information entropy, the probability of time effect microscopic state between vi and vj is denoted as

(

)

1

(

)

₍

₎

1, 2 , , , i j e

i j n n

i j

i i j j

L v v P v v

L v v

− = < = =

∑

∑

(1)

and the time effect entropy between vi and vj is

(

,

)

(

,

)

log2

(

,

)

e e e

i j i j i j

H v v = −P v v P v v . (2)

The total time effect entropy is summed as

(

)

1 1, 2 , n n e e i j i i j j

H H v v

−

= < =

=

∑ ∑

, (3)

and the biggest time effect entropy is

(

)

1 2 1, 2 log , n n em i j

i i j j

H L v v

−

= < =

 

= _{ }



∑ ∑

. (4)

Finally, the time effect order degree of the system is

1 e e em H O H

= − . (5)

Moreover, the probability of quality microscopic state of subsystem vi is define to be

( )

( )

( )

1 i q i n i i W v P v W v = =

V1

V2

V4

Vn

Vn-1

…

V3

V1

V2

V4

Vn

Vn-1

…

V3

[image:3.595.168.469.88.249.2]

(a) (b)

Figure 1. (a) System structure neglects directed information flow; (b) System structure

incorporates directed information flow.

( )

( )

log2

( )

q q q

i i i

H v = −P v P v . (7)

The total quality entropy is summed as

( )

1 n

q q

i i

H H v

=

=

∑

, (8)

and the biggest quality entropy is

( )

2 1

log

n qm

i i

H W v

=

=

∑

. (9)

Finally, the quality order degree of the system is

1

q q

qm

H O

H

= − . (10)

Thus, order degree of the system is synthesized as

e q

O=O +O . (11)

From the above expressions, we can find that: 1) the computation of time effect entropy regards the informa-tion flow between two arbitrary subsystems non-direcinforma-tional, but informainforma-tion flow between subsystems is de-signed to be directed in reality to ensure the timeliness of information; 2) the calculation of quality entropy con-siders that all subsystems correlated with vi influence the information quality of vi, but in reality information

quality of subsystem vi is only affected by its direct upstream systems. The fundamental reason of the above two

problems is that directions of information flow are neglected. Thus, the algorithms of L(vi, vj) and W(vi) need to

be revised. Order degree evaluation, which takes directions of information flow into account, is more in line with the actual structure of information system.

3. Improved Structural Entropy Model

Based on previous research on structural entropy and order degree, the paper proposes improved structural en-tropy to evaluate order degree of information system. The real-world structure of information system is shown as Figure 1(b). The set of information subsystems is marked as V ={ ,v v_{1 2},,vn} where vi represents a

sub-system. There is an edge eijbetween vi and vj if information passes from vito vj, and viand vj respectively stand

for the start and end of edge eij. There exist two edges eij and eji if information flow is bidirectional. The

in-degree of vi is computed as the number of upstream systems of vi, denoted as d−(vi). The path that information

passes from vi to vjis denoted by P v v

(

i, j

)

={ ,v ei im,v em, mn,vn,, ,v e vt tj, j} where vertexes and edges are

non-redundant. The number of edges in P(vi, vj) represents length of the path, and length of the shortest path

from vi to vj is denoted by L(vi, vj). L(vi, vj) may not be equal to L(vj, vi) for directed information flow between

Improved structural entropy model measures order degree of information system through time effect entropy and quality entropy which separately reflect level of timeliness and accuracy of information. Specifically, im-proved time effect entropy redefines time effect microscopic state between subsystems while imim-proved quality entropy revises quality microscopic state of each subsystem.

3.1. Improved Time Effect Entropy Model

The probability of correlated time effect microscopic state from vi to vj is denoted as

(

)

1

₍

(

₎

)

1

₍

₎

1, 2 2, 1

, ,

, ,

i j e

i j n n n n

i j i j

i i j j i i j j

L v v

P v v

L v v L v v

− −

= < = = > =

=

+

∑

∑

∑

∑

, (12)

where 1

(

)

1

(

)

1, 2 , 2, 1 ,

n n n n

i j i j

i i j j L v v i i j j L v v

− −

= < = + = > =

∑

∑

∑

∑

represents the total time effect microscopic state and L (vi, vj) denotes the time effect microscopic state from vi to vj. The shortest path from vi to vj may differ from the

shortest path from vj to vi. Thus, distinguishing time effect microscopic state and its probability between vi and vj

is necessary.

The time effect entropy from vi to vj is

(

,

)

(

,

)

log2

(

,

)

e e e

i j i j i j

H v v = −P v v P v v , (13)

and the total time effect entropy is summed as

(

)

(

)

1 1

1, 2 2, 1

, ,

n n n n

e e e

i j i j

i i j j i i j j

H H v v H v v

− −

= < = = > =

=

∑ ∑

+

∑ ∑

. (14)

The biggest time effect entropy is

(

)

(

)

1 1

2

1, 2 2, 1

log , ,

n n n n

em

i j i j

i i j j i i j j

H L v v L v v

− −

= < = = > =

 

= _ + _



∑ ∑

∑ ∑

. (15)

The time effect order degree of system is defined to be

1 e e em H O H

= − . (16)

3.2. Improved Quality Entropy Model

Quality entropy of subsystem vi is defined as

( )

( )

( )

1 i q i n i i d v P v d v − − = =

∑

, (17) d−(vi) is called the quality microscopic state of vi, which is equal to the number of its direct upstream systems.

Let

( )

1

n i d vi

− =

∑

denote the total quality microscopic state. Quality entropy of vi is

( )

( )

log2

( )

q q q

i i i

H v = −P v P v , (18)

the total quality entropy is summed as

( )

1 n i q q i

H H v

=

=

_∑

, (19)

and the biggest quality entropy is

( )

2 1 log n i qm i

H d− v

=

=

∑

. (20)

1

q q

qm

H O

H

= − , (21)

and order degree of the system is synthesized as

e q

O=O +O . (22)

Within a certain range, the bigger the order degree is, the system is more likely to provide high quality infor-mation.

4. Case Study

4.1. Problems Description

To illustrate the proposed model and compare order degree under the two scenarios, the paper implements our model in an elevator manufacturing enterprise. The enterprise comes to realize that direction of information flow between subsystems can heavily impact on timeliness and accuracy of information. Moreover, to quickly re-sponse to dynamic environment, the enterprise has to combing information flow between subsystems in order to improve chaotic state in transferring information. Figure 2(b) shows the current structure of information system in the enterprise. To facilitate our research, research object is the system at the application level which does not contain operating system, safety management system and other systems. As shown in Figure 2(b), there are eleven subsystems and each subsystem does not integrate other subsystems.

According the evaluation method of order degree in literature [6], the information flow between two subsys-tems is non-directional, and the corresponding structure is displayed as Figure 2(a). In fact, information flow has definite directions which affects the timeless and accuracy of information by altering the shortest path be-tween any two systems and in-degree of each system.

4.2. Results Analysis

1) From Table 1, we obtain that time effect order degree of information system increases under the directed information flow, which indicates the information system with definite direction of transferring information is more effectively to guarantee the timeliness of information. Theoretically, homogeneous information flow shortens the shortest path between subsystems and then improves timeliness of information. However, too much direct upstream systems make each subsystem analyzes and verifies per unit information blindly and randomly, which consumes a lot of time. Directed information flow makes information transition more definite and fluent so that information can be transmitted in order. Thus, the value of time effect order degree increases from 0.1224 to 0.1360.

2) Similarly, from Table 2, we find that directed information flow reduces quality order degree, which means the information system with definite direction of transferring information is less effectively to guarantee the ac-curacy of information. Homogeneous information flow makes each subsystem have more direct upstream sys-tems so that system analyzes and verifies per unit information that passing from its directed upstream system repeatedly. Consequently, quality degree of information system decreases from 0.4050 to 0.4040.

(1) E-commerce Platform

(2)The Integrated System of CAD, CAE, CAPP and CAM

(3) Customer Relationship

Management (CRM) System Management (SCM) System(4) Supply Chain

(5) Product Lifecycle Management (PLM)

System

(6) Enterprise Resource Planning (ERP) System

(7) Human Resource (HR) System

(8) Office Automation (OA)

System

(9) Manufacturing Execution System

(MES)

(10) Machine to Machine (M2M)

System

(11) Knowledge Management (KM) System

(a)

(1) E-commerce Platform

(2)The Integrated System of

CAD, CAE, CAPP and CAM Management (CRM) System(3) Customer Relationship Management (SCM) System(4) Supply Chain

(5) Product Lifecycle Management (PLM)

System

(6) Enterprise Resource Planning (ERP) System

(7) Human Resource (HR) System

(8) Office Automation (OA)

System

(9) Manufacturing Execution System

(MES)

(10) Machine to Machine (M2M)

System

(11) Knowledge Management (KM) System

[image:6.595.96.517.83.648.2]

(b)

Figure 2. (a) System structure neglects directed information flow; (b) System structure incorporates directed

information flow.

[image:7.595.86.541.111.503.2]

Table 1. A comparison between both time effect entropy appraisal.

Oe _L(v

i, vj) Number Microscopic state Pe(vi, vj) He(vi, vj)

i < j

1 22 22 0.0111 0.0721 2 31 62 0.0222 0.1220 3 2 6 0.0333 0.1634 a He _{= 5.6973 H}em _{= 6.4919 O}e _{= 0.1224}

i < j

1 21 21 0.0048 0.0370 2 22 44 0.0096 0.0643 3 10 30 0.0144 0.0881 4 2 8 0.0192 0.1095

i > j

1 16 16 0.0048 0.0370 2 28 54 0.0096 0.0643 3 10 30 0.0144 0.0881 4 1 4 0.0192 0.1095 b He _{= 6.6590 H}em _{= 7.7077 O}e _{= 0.1360}

Table 2. A comparison between both quality entropy appraisal.

Oq _W(v

i) Number Microscopic state Pq(vi) Hq(vi)

2 4 8 0.0455 02028 3 2 6 0.0682 0.2642 4 2 8 0.0909 0.3145 6 1 6 0.1364 0.3894 7 1 7 0.1591 0.4219 9 1 9 0.2045 0.4683 a Hq = 3.2482 Hqm = 5.4594 Oq = 0.4050

Oq _d−_(v

i) Number Microscopic state Pq(vi) Hq(vi)

1 3 3 0.0270 0.1407 2 2 4 0.0540 0.2274 3 3 9 0.0810 0.2937 6 2 12 0.1620 0.4254 9 1 9 0.2430 0.4960 b Hq _{= 3.1408 H}qm _{= 5.2095 O}q _{= 0.4040}

information flow in enterprise organization structure speeds up delivery of information, but it reduces informa-tion sources of each decision-making agent, which ultimately make decision makers acquire lower accurate in-formation. Improved structural entropy suits better to actual structure of information system and research results will facilitate management activities.

5. Conclusions

[image:7.595.88.540.333.573.2]

a number of managerial insights. First, given that directed information flow effectively improves the timeliness, the enterprise needs to ensure that its information system and organizational structure have definite directions to transfer information. Only in this way can enterprise sensitively percept the environmental change and quickly response to it. Second, specifying the direction of transferring information may reduce the accuracy of informa-tion, but it decreases cost through reducing blind, random and repeated analysis and verification of information from the direct upstream systems. If the reduced cost exceeds the loss caused by the decreased accuracy of in-formation, specifying direction of information system will have a positive effect on information system. Last but not least, a company cannot owe the timeliness and accuracy at the same time, but the accuracy of information is the premise to the development of enterprises. On condition that accuracy of information can satisfy require-ments, enterprise can take action to enhance its sensitivity to response to the external requirements and to achieve the foregoing advantages, which is significant to a responsive organization. In addition, within a certain range, increasing the order degree will improve the operation efficiency of systems. The order degree beyond the range indicates the instability of systems. Thus, enterprise should keep the order degree within a reasonable range to maintain the stable operation of systems.

Considering the actual situation, this paper proposes an improved algorithm of the structure entropy model to evaluate the order degree of information system from a micro level, which increases the reliability of order de-gree. The improved structural entropy model is suitable not only for the information system, but also for other sys- tems such as organizational system and transport system. However, assessment of order degree should be multi- angles, which is one of the following research focuses. Moreover, self-organization evolvement of information system, resource configuration process and robustness analysis of information system are also research focuses in the future.

Acknowledgements

Authors would like to acknowledge the financial support from National Natural Science Foundation of China (No. 50675069).

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